Optimal array element localization

Advanced array processing methods require accurate knowledge of the location of individual elements in a sensor array. Array element localization (AEL) methods are typically based on inverting acoustic travel-time measurements from a series of controlled sources at well-known positions to the sensors to be localized. An important issue in AEL is designing the configuration of source positions: a well-designed configuration can produce substantially better sensor localization than a poor configuration. In this paper, the effects of the source configuration and of errors in the data, source positions, and ocean sound speed are quantified using a sensor-position error measure based on the a posteriori uncertainty of a general formulation of the AEL inverse problem. Optimal AEL source configurations are determined by minimizing this error measure with respect to the source positions using an efficient hybrid optimization algorithm. This approach is highly flexible, and can be applied to any sensor configuration and combination of errors; it is also straightforward to apply constraints to the source positions, or to include the effects of data errors that vary with range. The ability to determine optimal source configurations as a function of the number of sources and of the errors in the data, source positions, and sound speed allows the effects of each of these factors to be examined quantitatively in a consistent manner. A modeling study considering these factors can guide in the design of AEL systems to meet specific objectives for sensor localization.